Abstract
Let ℛ be a commutative ring with unity and let ℬ be a unitary R-module. Let ℵ be a proper submodule of ℬ, ℵ is called semisecond submodule if for any r∈ℛ, r≠0, n∈Z+, either rnℵ=0 or rnℵ=rℵ.
 In this work, we introduce the concept of semisecond submodule and confer numerous properties concerning with this notion. Also we study semisecond modules as a popularization of second modules, where an ℛ-module ℬ is called semisecond, if ℬ is semisecond submodul of ℬ.
Highlights
Let R be a commutative ring with unity and let B be a unitary R -module
We survey the relationships between semisecond submodules and other submodules
We survey the relationships between semisecond submodules and some kind of submodules
Summary
Let R be a commutative ring with unity and let B be a unitary R -module. S.Yass in [1]introduced the notation of second submodule and second module where a submodule א of an R -module B is called second submodule if for every r∈R, r≠0, either rא =א or rא =0 and a module B is called semisecond if B is semisecond submodule of B. Proof: -Let א be a S.R.M. B such that א is second submodule, that is r א =0 or r א = א for every r∈R, r≠0. Proposition (4):-If א is a semisecond S.R.M. B such that B is torsion free over an I.D. R, א is a second submodule.
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